Fedunov R.G., Yermolenko I.P. Accelerated Calculation of Integrals in the Theory of Non-Thermal Electron Transfer

Details
Hits: 565

https://doi.org/10.15688/mpcm.jvolsu.2018.3.5

Roman Gennadyevich Fedunov
Candidate of Physical and Mathematical Sciences, Associate Professor,
Department of Theoretical Physics and Wave Processes,
Volgograd State University
This email address is being protected from spambots. You need JavaScript enabled to view it. , This email address is being protected from spambots. You need JavaScript enabled to view it.
Prosp. Universitetsky, 100, 400062 Volgograd, Russian Federation

Igor Petrovich Yermolenko
Master Student, Department of Theoretical Physics and Wave Processes,
Volgograd State University
This email address is being protected from spambots. You need JavaScript enabled to view it. , This email address is being protected from spambots. You need JavaScript enabled to view it.
Prosp. Universitetsky, 100, 400062 Volgograd, Russian Federation

Abstract. In this article we’ve carried out a modification of the expression for calculating the probability of non-thermal electron transfer in a two-level system obtained in the framework of the nonstationary second-order perturbation theory for electron interaction. This expression takes into account the reorganization of the environment (Debye model) and high-frequency intramolecular vibrational modes (quantum mechanical description). Since the “Debye” part is characterized by slow relaxation times, which significantly exceed the period of intramolecular vibrations, the “quantum” part will be a rapidly oscillating function included in the integral. As a result, computing two-dimensional integral using simple grid methods may require significant computational resources. To speed up the calculation of this integral, we propose a Gauss quadrature formula. It is shown that, in the high-temperature limit, the quadrature formula can be successfully applied in the theory of non-thermal electron transfer and increases the calculation speed of the integral by two orders of magnitude.

Key words: electron transfer, nonstationary perturbation theory, quadrature formula, intramolecular high-frequency modes.

Creative Commons License
Accelerated Calculation of Integrals in the Theory of Non-Thermal  Electron Transfer by Fedunov R.G., Yermolenko I.P. is licensed under a Creative Commons Attribution 4.0 International License.

Citation in English: Mathematical Physics and Computer Simulation. Vol. 21 No. 3 2018, pp. 48-57

Attachments:
Download this file (1_Fedunov_Ermolenko.pdf) 1_Fedunov_Ermolenko.pdf
URL: https://mp.jvolsu.com/index.php/en/component/attachments/download/823		732 Downloads